Factor

3a\left(x-4\right)\left(x+1\right)

$3a(x−4)(x+1)$

Evaluate

3a\left(x-4\right)\left(x+1\right)

$3a(x−4)(x+1)$

Graph

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3\left(ax^{2}-3ax-4a\right)

Factor out 3.

a\left(x^{2}-3x-4\right)

Consider ax^{2}-3ax-4a. Factor out a.

p+q=-3 pq=1\left(-4\right)=-4

Consider x^{2}-3x-4. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+px+qx-4. To find p and q, set up a system to be solved.

1,-4 2,-2

Since pq is negative, p and q have the opposite signs. Since p+q is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -4.

1-4=-3 2-2=0

Calculate the sum for each pair.

p=-4 q=1

The solution is the pair that gives sum -3.

\left(x^{2}-4x\right)+\left(x-4\right)

Rewrite x^{2}-3x-4 as \left(x^{2}-4x\right)+\left(x-4\right).

x\left(x-4\right)+x-4

Factor out x in x^{2}-4x.

\left(x-4\right)\left(x+1\right)

Factor out common term x-4 by using distributive property.

3a\left(x-4\right)\left(x+1\right)

Rewrite the complete factored expression.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

Matrix

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \right]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $